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During the holiday season, the world’s biggest online retailer said “tens of millions of people worldwide” signed up for its Prime service, and in the U.S. alone, more than 1 billion items were shipped for free using Prime.

(Bloomberg)—Amazon.com Inc. reported a record-breaking holiday season as shoppers loaded their online baskets with items from the Echo speaker to Calvin Klein clothes, suggesting consumer optimism isn’t being deterred by a tumbling stock market.

The world’s biggest online retailer said “tens of millions of people worldwide” signed up for its Prime service, which offers free two-day shipping on millions of items as well as video and music streaming. In the U.S. alone, more than 1 billion items were shipped for free using Prime, Amazon said in a statement Wednesday.

The U.S. was already headed into a blow-out Christmas shopping spree, as Americans are benefiting from higher employment and wages, fueling higher household cash flow. Consumers seemed to be merry despite an S&P 500 Index that has tumbled, a government shutdown that’s entering its fifth day and ongoing trade tensions with China.

People bought “millions more” of Amazon’s own devices compared with last year, including the new Echo Dot speaker and the Fire TV Stick, the Seattle-based company said. At the same time, Amazon said more than 50% of items sold in its stores came from small and medium-sized businesses.

Among the most popular items under the Christmas tree were the L.O.L. Surprise! Glam Glitter Series doll, Bose Corp. wireless headphones and clothes from Carhartt Inc. Other popular brands bought through Amazon’s Prime Wardrobe service, which allows consumers to fill a box with selected items and return anything that they don’t want, included PVH Corp.’s Calvin Klein, and Hanesbrands Inc.’s Champion.

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Amazon started the shopping frenzy out strong, with November’s Cyber Monday already pegged as the company’s biggest shopping day in history. Along with the Christmas sales report, the picture seems much brighter than Amazon had initially projected in its latest earnings results. In October, Amazon’s revenue and profit forecast for the holiday quarter fell short of analysts’ estimates, as investors worried about Amazon’s increased pace of spending.

While Amazon has expanded into almost every area of retail, from pharmaceuticals to groceries, its more profitable units are cloud computing and advertising. Still, Amazon, which dominates e-commerce in the U.S., has relied on the growth of its Prime members, who pay $119 a year for the service. Recent estimates put subscribers at just under 100 million in the U.S. Amazon didn’t give any new numbers for Prime subscribers in its statement Wednesday, but said millions of unique items in the U.S. shipped with Prime.

That kind of volume presents a challenge for logistics services like FedEx Corp. and United Parcel Service Inc. In 2013, a larger than expected surge in last-minute online shopping caught UPS off guard and forced it and Amazon and other retailers to offer refunds to customers who didn’t receive their orders on time for Christmas.

This year, UPS said it expects to deliver an average of more than 31 million parcels a day during the holidays and anticipates a peak-season total of about 800 million packages to rise 5% compared with last year’s tally. To deal with the rush of deliveries, the company invested in automation and new facilities to add sorting capacity of 350,000 packages an hour to its U.S. system.

“We’re so far pleased with the operational aspect of it,” said Glenn Zaccara, a spokesman for UPS. “The investments that UPS made in the network, technology, people and planning across the season with our customers obviously paid off.”

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The couriers are bracing for a second wave of business as people begin returning gifts in January. UPS expects return packages to hit 1.3 million on Jan. 3. The company said it had 1.5 million returns, its highest for the season, on Dec. 19.

With the S&P teetering on a bear market after a volatile fourth quarter and the worst December in more than a decade, Baird analyst Colin Sebastian lists Amazon as one of the three best picks for investors in the event of a market rebound. Amazon shares were up 2.8%, to $1,381 in New York Wednesday morning. They have gained about 19% this year, compared with an 11% decline on the S&P.

If Amazon’s Echo speaker was one of its best sellers, it appears to also have been a victim of its own success. Powered by Alexa, the voice-activated software, the smart devices appeared overwhelmed by an onslaught of new users on Christmas, according to reports from the U.K. Owners asking Alexa to play music, turn on the tree lights or recite turkey recipes were often met with the highly unsatisfactory response of: “Sorry, I’m having trouble understanding you right now,” The Guardian reported.

A week before Christmas, several of Amazon’s online stores in North America and Europe sold out of various models of Alexa-powered devices, hinting at the surge in demand.